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A constitutive model for anisotropic materials based on Neuber's rule

机译：基于Neuber法则的各向异性材料本构模型

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Phenomenological approaches to fatigue damage prediction often rely on the assessment of local stress-strain concentrations in structural components. To avoid complex plastic analysis in fatigue assessment, approximate constitutive models have been developed to evaluate the local inelastic response of the material and which allow for an adequate lifetime prediction in a competitive time. One of these approximate methods is the Neuber rule, which has originally been elaborated for the uniaxial loading state of isotropic materials. This paper addresses an approximate method for multiaxial loading of anisotropic materials. The proposed approach is based on a tensorial formulation of the Ramberg-Osgood equation and a generalization of the uniaxial Neuber hypothesis by assuming the equivalence of the deviatoric strain energy density for the elastic and inelastic solution in the notch region. After a decomposition of the stress tensor into a normalized direction tensor and a stress invariant, a nonlinear expression is obtained which can be iterated for the unknown inelastic stress state. It is shown that the proposed anisotropic Neuber rule includes the multiaxial isotropic and the classical uniaxial formulation as special cases. Furthermore, aspects of parameter identification are discussed for directionally solidified Nickel-based superalloys with transverse isotropic properties and single crystal materials with cubic anisotropy. Two numerical examples demonstrate the applicability of the proposed approach.
机译：疲劳损伤预测的现象学方法通常取决于对结构部件中局部应力应变浓度的评估。为了避免在疲劳评估中进行复杂的塑性分析，已经开发了近似的本构模型来评估材料的局部非弹性响应，并且可以在竞争时间内进行足够的寿命预测。这些近似方法之一是Neuber规则，该规则最初是针对各向同性材料的单轴加载状态而精心设计的。本文提出了各向异性材料多轴加载的一种近似方法。所提出的方法是基于Ramberg-Osgood方程的张量公式和单轴Neuber假设的一般化，并假设缺口区域中弹性和非弹性解的偏应变能量密度相等。在将应力张量分解为归一化方向张量和应力不变量后，获得了可以对未知的非弹性应力状态进行迭代的非线性表达式。结果表明，所提出的各向异性诺贝尔规则包括多轴各向同性和经典单轴公式，作为特殊情况。此外，还讨论了具有横向各向同性特性的定向凝固镍基高温合金和具有立方各向异性的单晶材料的参数识别方面。两个数值例子证明了该方法的适用性。

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